Entire solution in cylinder-like domains for a bistable reaction-diffusion equation

Antoine Pauthier

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arXiv · 1604.00928

Entire solution in cylinder-like domains for a bistable reaction-diffusion equation

Antoine Pauthier

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Abstract

We construct nontrivial entire solutions for a bistable reaction-diffusion equation in a class of domains that are unbounded in one direction. The motivation comes from recent results of Berestycki, Bouhours, and Chapuisat concerning propagation and blocking phenomena in infinite domains. A key assumption in their study was the "cylinder-like" assumption: their domains are supposed to be straight cylinders in a half space. The purpose of this paper is to consider domains that tend to a straight cylinder in one direction. We also prove the existence of an entire solution for a one-dimensional problem with a non-homogeneous linear term.

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Antoine Pauthier. 2016-04-04. Entire solution in cylinder-like domains for a bistable reaction-diffusion equation. https://arxiv.org/abs/1604.00928

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